The paper presents a theoretical study of the harmonic power evolution in a single-pass free-electron laser (FEL) and a comparison with some of the experimental results. The phenomenological approach which considers the main FEL parameters (current density, the Lorentz factor, electron energy spread, and the beam geometry) provides a description of any undulator. With due regard to the real laser beam parameters, the effect from high-order harmonic radiation and the beam deviation from the undulator axis on the FEL irradiation is investigated. The Bessel coefficients are calculated for the undulator in the presence of the second periodic field. The phenomenological approach provides the free-electron laser simulation experiments at Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC), SPring-8 Angstrom Compact Free-Electron Laser (SACLA) and Linac Coherent Light Source (LCLS). These studies include the high-harmonic generation, a comparison of the emission power evolution with the experimentally obtained data on the harmonic generation including even and odd high-order harmonics, gain and saturation lengths and the respective power. A possible effect from the third harmonic of the planar undulator magnetic field is studied in relation to the FEL irradiation. It is shown that this effect is insignificant even at the magnetic-field harmonic amplitude equaling ~1/10 of the amplitude of the ideal magnetic field in the periodic undulator. It is found that the second-harmonic generation in FEL lasing is rather weak, that is in good agreement with the measurement results as well as the behavior of the high-order harmonics.
Similar content being viewed by others
References
V. L. Ginzburg, Izv. Akad. Nauk, Fiz., 11, No. 2, 1651 (1947).
H. Motz, W. Thon, and R. N.J. Whitehurst, Appl. Phys., 24, 826 (1953).
B. W.J. McNeil and N. R. Thompson, Nat. Photonics, 4, 814 (2010).
V. G. Bagrov, G. S. Bisnovatyi-Kogan, V. A. Bordovitsyn, et al., A Theory of Relativistic Particle Radiation [in Russian], Fizmatlit, Moscow (2002), 575 p.
S. C. Bajt and M. A. Wall, PCT No. PCT/US2000/013549 (2000) and PCT No. EP 1198725A1 (2002).
P. Sprangle and R. A. Smith, Phys. Rev. A, 21, No. 1, 293 (1980).
L.-H. Yu et al., Science, 289, 932 (2000).
K. V. Zhukovsky, Russ. Phys. J., 60, No. 9, 1630–1637 (2017).
G. Dattoli, J. Appl. Phys., 84, Nо. 5, 2393–2398 (1998).
G. Dattoli, L. Giannessi, P. L. Ottaviani, and C. Ronsivalle, J. Appl. Phys., 95, 3206–3210 (2004).
E. A. Schneidmiller and M. V. Yurkov, Phys. Rev. ST Accel. Beams, 15, 080702 (2012).
G. Dattoli and P.L. Ottaviani, Opt. Commun., 204, No. 1, 283–297 (2002).
K. Zhukovsky and I. Potapov, Laser Part. Beams, 35, 326 (2017).
K. Zhukovsky, J. Phys. D: Appl. Phys., 50, 505601 (2017).
K. Zhukovsky, J. Appl. Phys., 122, No. 23, 233103 (2017).
K. Zhukovsky, Opt. Commun., 418, 57–64 (2018).
K. V. Zhukovsky, I. A. Potapov, and A. M. Kalitenko, Radiophys. Quant. El., 61, No. 3, 216–231 (2018).
K. V. Zhukovsky, Vestnik MGU. Ser. 3. Fizika. Astronomiya. No. 4, 26–34 (2018).
K. V. Zhukovsky, Vestnik MGU. Ser. 3. Fizika. Astronomiya. No. 5, 18–25 (2018).
K. V. Zhukovsky, Russ. Phys. J., 61, No. 2, 278–286 (2018).
K. Zhukovsky, EPL, 119, 34002 (2017).
L. Giannessi et al., Phys. Rev. ST Accel. Beams, 14, 060712 (2011).
Shigeki Owada et al., J. Synchrotron Rad., 25, 282–288 (2018).
P. Emma et al., Nat. Photonics, 4, 641–647 (2010).
K. Zhukovsky and A. Kalitenko, J. Synchrotron Rad., 26, 159–169 (2019), DOI: https://doi.org/10.1107/S1600577518012444.
K. Zhukovsky, J. Optics, 20, Nо. 9, 095003 (2018).
D. Ratner et al., Phys. Rev. ST Accel. Beams, 14, 060701 (2011).
K. Lee, J. Mun, S. Hee Park, et al., Nucl. Instrum. Methods Phys. Res. A, 776, 27–33 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 153–160, February, 2019.
Rights and permissions
About this article
Cite this article
Zhukovsky, K.V., Kalitenko, A.M. Harmonic Generation in Planar Undulators in Single-Pass Free Electron Lasers. Russ Phys J 62, 354–362 (2019). https://doi.org/10.1007/s11182-019-01719-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-019-01719-7